Use the accompanying data set to find the quartiles. 62 54 61 55 64 56 61 63 56 57 60 58 57 73 77

To find the quartiles, the steps are as follows:

1. **Order the data set from smallest to largest**.
2. **Find the median (Q2)**, which splits the data set into two halves.
3. **Find Q1 (first quartile)**, which is the median of the lower half of the data.
4. **Find Q3 (third quartile)**, which is the median of the upper half of the data.

### Step 1: Sort the data set
The data set in ascending order is:

54, 55, 56, 56, 57, 57, 58, 60, 61, 61, 62, 63, 64, 73, 77

### Step 2: Find the median (Q2)
The median is the middle value. Since there are 15 numbers, the median is the 8th number:

\[ \text{Median} = Q2 = 60 \]

### Step 3: Find Q1 (first quartile)
Q1 is the median of the lower half of the data (numbers before the median):

54, 55, 56, 56, 57, 57, 58

The median of this lower half is the 4th number:

\[ Q1 = 56 \]

### Step 4: Find Q3 (third quartile)
Q3 is the median of the upper half of the data (numbers after the median):

61, 61, 62, 63, 64, 73, 77

The median of this upper half is the 4th number:

\[ Q3 = 63 \]

### Summary of Quartiles:
- **Q1 (First Quartile):** 56
- **Q2 (Median):** 60
- **Q3 (Third Quartile):** 63

Let me know if you'd like more details or have any questions.

Here are 5 related questions:
1. What is the interquartile range (IQR) for this data set?
2. How do outliers affect the quartiles in a data set?
3. Can you calculate the mean and standard deviation of this data set?
4. How are quartiles used in box plots?
5. What is the difference between quartiles and percentiles?

**Tip:** Quartiles help identify the spread of data and highlight outliers when combined with measures like the IQR.

Learn how to calculate the first, second (median), and third quartiles for the data set 62, 54, 61, 55, 64, 56, 61, 63, 56, 57, 60, 58, 57, 73, 77. This tutorial provides a step-by-step solution and covers important statistical concepts like Q1, Q2, and Q3. Suitable for students in Grades 6-8.

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